An inference method is proposed, which can control the degree to which the fuzzy constraints of given facts are propagated to those of consequences via the nonlinear mapping represented by fuzzy rules. The conventional method, α-GEMST (α-level-set and generalized-mean-based inference in synergy with composition via linguistic-truth-value control), has limitations in the control of the propagation degree. In contrast, the proposed method can fully control the fuzzy-constraint propagation to a different degree with each fuzzy rule. After the nonlinear mapping, the proposed method performs fuzzy-logic-based control for further fuzzy-constraint propagation wherein evaluations are conducted via linguistic truth values to suppress the excessive specificity decrease in deduced consequences. Thereby, fuzzy constraints can be propagated in various ways by selecting one pair from the widely available implications and compositional operations. The proposed method controls the fuzzy-constraint propagation at the multi-levels of α in its α-cut-based operations. This scheme contributes to fast computation with parallel processing for each level of α. Simulation results illustrate that the proposed method can properly control the propagation degree. The proposed method is expected to be applied to the modeling of given systems with various fuzzy input-output relations.